updated 07/28/2010 AT 12:00 PM ET
•originally published 07/28/2010 AT 12:35 PM ET
Kate Winslet reportedly has a new man.
Winslet and Dowler, also 34, who has appeared in fashion campaigns for Burberry and Paul Smith, have “been on lots of dates and get on really well. It’s early days for them but they enjoy each other’s company,” a source tells the British tabloid.
Reps for the Oscar winner and the model had no comment about the report.